Polytropic models of filamentary interstellar clouds - I. Structure and stability

The properties of filamentary interstellar clouds observed at submillimetre wavelengths, especially by the Herschel Space Observatory, are analysed with polytropic models in cylindrical symmetry. The observed radial density profiles are well reproduced by negative-index cylindrical polytropes with polytropic exponent 1/3 less than or similar to gamma(p) less than or similar to 2/3 (polytropic index -3 less than or similar to n less than or similar to -3/2), indicating either external heating or non-thermal pressure components. However, the former possibility requires unrealistically high gas temperatures at the filament's surface and is therefore very unlikely. Non-thermal support, perhaps resulting from a superposition of small-amplitude Alfven waves (corresponding to gamma(p) = 1/2), is a more realistic possibility, at least for the most massive filaments. If the velocity dispersion scales as the square root of the density (or column density) on the filament's axis, as suggested by observations, then polytropic models are characterized by a uniform width. The mass per unit length of pressure-bounded cylindrical polytropes depends on the conditions at the boundary and is not limited as in the isothermal case. However, polytropic filaments can remain stable to radial collapse for values of the axis-to-surface density contrast as large as the values observed only if they are supported by a non-isentropic pressure component.